In this essay, I present an alternative explanation for the cosmic acceleration which appears as a consequence of recent high redshift Supernova data. In the usual interpretation, this cosmic acceleration is explained by the presence of a positive cosmological constant or vacuum energy, in the background of Friedmann models. Instead, I will consider a Local Rotational Symmetric (LRS) inhomogeneous spacetime, with a barotropic perfect fluid equation of state for the cosmic matter. Within this framework the kinematical acceleration of the cosmic fluid or, equivalently, the inhomogeneity of matter, is just the responsible of the SNe Ia measured cosmic acceleration. Although in our model the Cosmological Principle is relaxed, it maintains local isotropy about our worldline in agreement with the CBR experiments. a This essay received an "Honorable Mention" in the 1999 Essay Competition of the Gravity Research Foundation.

Today, the Global Navigation Satellite Systems, used as global positioning systems, are the GPS and the GLONASS. They are based on a Newtonian model and hence they are only operative when several relativistic effects are taken into account. The most important relativistic effects (to order 1/c 2 ) are: the Einstein gravitational blue shift effect of the satellite clock frequency (Equivalence Principle of General Relativity) and the Doppler red shift of second order, due to the motion of the satellite (Special Relativity). On the other hand, in a few years the Galileo system will be built, copying the GPS system unless an alternative project is designed. In this work, it will be also shown that the SYPOR project, using fully relativistic concepts, is an alternative to a mere copy of the GPS system. According to this project, the Galileo system would be exact and there would be no need for relativistic corrections.

A vJ/c correction to the Shapiro time delay seems verified by a 2002 Jovian observation by VLBI. In this Essay, this correction is interpreted as an effect of the aberration of light in an optically refractive medium which supplies an analog of Jupiter's gravity field rather than as a measurement of the speed of gravity, as it was first proposed by other authors. The variation of the index of refraction is induced by the Lorentz invariance of the weak gravitational field equations for Jupiter in a uniform translational slow motion with velocity vJ=13.5 km / s . The correction on time delay and deflection is due not to the Kerr (or Lense-Thirring) stationary gravitomagnetic field of Jupiter, but to its Schwarzschild gravitostatic field when measured from the barycenter of the solar system.

In this paper, it is shown, using a geometrical approach, the isotropy of the velocity of light measured in a rotating frame in the Minkowski space-time, and it is verified that this result is compatible with the Sagnac effect. Furthermore, we find that this problem can be reduced to the solution of geodesic triangles in a Minkowskian cylinder. A relationship between the problems established on the cylinder and on the Minkowskian plane is obtained through a local isometry.

In the last years, the peculiar velocities of many X-ray galaxies clusters with respect to the distance have been measured directly in the rest frame of the cosmic microwave background radiation (CBR), using the kinematic Sunyaev-Zeldovich (kSZ) effect. These measures prove that exists a highly coherent motion, extending out to at least to 1 Gpc, of the matter rest frame with respect to the CBR rest frame. This global motion was named "dark flow". By using an inhomogeneous spherically symmetric "tilted" Lemaître model, we could explain the dark flow if we assume a linear increase with distance of the peculiar velocities, which is in principle allowed by these observations. This linear increase of the dark flow with the distance has the same behavior that the intrinsic dipole, due to the kinematic acceleration, which appears in the Hubble law of the Lemaître model. In the "tilted" Lemaître model considered, we consider that the radiation orthogonal congruence is a perfect fluid and the matter "tilted" congruence is an imperfect fluid with heat flux. Tilted cosmological modelsIn cosmology it is essential to specify the set of observers, or rather, the congruences of world-lines from which observations are made.Cosmological quantities depend on the choice of these congruences, specified by 4-velocities fields. For instance, with the same spacetime metric, one can have two different stress-energy-momentum tensors, corresponding to two different congru-